Find the Derivative - d/dx y=(7 square root of x)/8

Problem

d()/d(x)(7√(,x))/8

Solution

1. Rewrite the expression by moving the constant coefficient 7/8 outside and converting the radical √(,x) to its exponential form x(1/2)

d()/d(x)(7*x(1/2))/8

2. Apply the constant multiple rule, which allows the constant 7/8 to be pulled in front of the derivative operator.

7/8d(x(1/2))/d(x)

3. Apply the power rule d(xn)/d(x)=n*x(n−1) where n=1/2

7/8⋅1/2*x(1/2−1)

4. Simplify the exponent by calculating 1/2−1=−1/2

7/16*x(−1/2)

5. Rewrite the expression using positive exponents by moving x(−1/2) to the denominator as √(,x)

7/(16√(,x))

Final Answer

d()/d(x)(7√(,x))/8=7/(16√(,x))

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